Sphinx is a free open-source SQL full-text PHP search engine designed
from the ground up with performance, relevance (aka search quality), and
integration simplicity in mind.

Sphinx lets you either batch index and search data stored in an SQL
database, NoSQL storage, or just files quickly and easily — or index and
search data on the fly, working with Sphinx pretty much as a database
server.

Sphider is a free OpenSource PHP search engine project which using MySQL
as its back database. Sphider is a great tool for adding search
functionality to your website or buliding your custom search engine, it
is a powerful PHP search engine.Sphider installed and modified easily,
and used in thousands of websites across the world.

OpenWebSpider ia a free PHP search engine project, OpenWebSpider uses
MySQL Server as the backend to store the index.The new released
OpenWebSpider v0.1.4 is featured with MP3s and PDFs support!
More PHP search engine you can check out:http://www.phpkode.com/projects/category/php-search-engine/